Certainly! Let's solve the problem step-by-step.
Question: An angle measures 38° less than the measure of its supplementary angle. What is the measure of each angle?
Solution:
1. Understand the relationship between supplementary angles:
- Two angles are supplementary if the sum of their measures is 180°. In other words, if you have two angles [tex]\( \alpha \)[/tex] and [tex]\( \beta \)[/tex], then [tex]\( \alpha + \beta = 180° \)[/tex].
2. Define the angles:
- Let the measure of the first angle be [tex]\( x \)[/tex].
- The measure of its supplementary angle will then be [tex]\( 180° - x \)[/tex].
3. Set up the equation based on the given information:
- We are told that the first angle is 38° less than its supplementary angle.
- Therefore, we can write the equation as:
[tex]\[
x = (180° - x) - 38°
\][/tex]
4. Solve the equation:
- Start by simplifying the right-hand side:
[tex]\[
x = 180° - x - 38°
\][/tex]
- Combine like terms:
[tex]\[
x + x = 180° - 38°
\][/tex]
- Simplify further:
[tex]\[
2x = 142°
\][/tex]
- Finally, solve for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[
x = \frac{142°}{2}
\][/tex]
[tex]\[
x = 71°
\][/tex]
5. Find the measure of the supplementary angle:
- The supplementary angle is:
[tex]\[
180° - 71° = 109°
\][/tex]
Conclusion:
The measure of the first angle is [tex]\( 71° \)[/tex] and the measure of the supplementary angle is [tex]\( 109° \)[/tex].
So, the measures of the two angles are [tex]\( 71° \)[/tex] and [tex]\( 109° \)[/tex].
